TY - JOUR
T1 - STOCHASTIC REPRESENTATIONS FOR SOLUTIONS TO PARABOLIC DIRICHLET PROBLEMS FOR NONLOCAL BELLMAN EQUATIONS
AU - GONG, Ruoting
AU - MOU, Chenchen
AU - ŚWIĘCH, Andrzej
PY - 2019/12
Y1 - 2019/12
N2 - We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
AB - We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
KW - Dynamic programming principle
KW - Hamilton-Jacobi-Bellman equation
KW - Integro-PDE
KW - Lévy process
KW - Stochastic representation formula
KW - Value function
KW - Viscosity solution
KW - Dynamic programming principle
KW - Hamilton-Jacobi-Bellman equation
KW - Integro-PDE
KW - Lévy process
KW - Stochastic representation formula
KW - Value function
KW - Viscosity solution
KW - Dynamic programming principle
KW - Hamilton-Jacobi-Bellman equation
KW - Integro-PDE
KW - Lévy process
KW - Stochastic representation formula
KW - Value function
KW - Viscosity solution
UR - http://www.scopus.com/inward/record.url?scp=85081936939&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85081936939&origin=recordpage
U2 - 10.1214/19-AAP1473
DO - 10.1214/19-AAP1473
M3 - 21_Publication in refereed journal
VL - 29
SP - 3271
EP - 3310
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 6
ER -